After 35 minutes into a race, Bobby has run ⁷₁₃ of the route while David has covered only ⁴₁₃ of the distance. Bobby runs at the same average speed throughout the race and David’s average speed is 78 m/min slower than Bobby’s. If David wants to finish the race at the same time as Bobby, by how many percent should he increase his average speed by for the remaining part of the race? Round off your answer to the nearest whole number.
Extra distance that Bobby ran more than David in first 35 min
= 35 x 78
= 2730 m

Fraction of the entire distance that was covered by Bobby more than David in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 3 = 910 m

Distance that David ran in the first 35 min
= 4 x 910
= 3640 m

David's average speed
= 3640 ÷ 35
= 104 m/min

Bobby's average speed
= 104 + 78
= 182 m/min

Fraction of the journey that Bobby needed to run to complete the race
= 1 - ⁷₁₃
= ⁶₁₃

¹₁₃ of the entire distance = 910 m
⁶₁₃ of the entire distance = 6 x 910 = 5460 m

Duration that Bobby would take to complete
= 5460 ÷ 182
= 30 min

Fraction of the journey that Bobby needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 910 = 8190 m  

Speed that David needs to take to complete distance at the same time as Bobby
= 8190 ÷ 30
= 273 m/min

Increase in David's average speed
= 273 - 104
= 169 m/min

Percentage increase in David's average speed
= ¹⁶⁹₁₀₄ x 100%
≈ 163%

Answer(s): 163%